Reliable Reasoning Beyond Natural Language

Despite their linguistic competence, Large Language models (LLMs) often exhibit limitations in their ability to reason reliably and flexibly. To address this, we propose a neurosymbolic approach that prompts LLMs to extract and encode all relevant information from a problem statement as logical code statements, and then use a logic programming language (Prolog) to conduct the iterative computations of explicit deductive reasoning. Our approach significantly enhances the performance of LLMs on the standard mathematical reasoning benchmark, GSM8k, and the Navigate dataset from the BIG-bench dataset. Additionally, we introduce a novel dataset, the Non-Linear Reasoning (NLR) dataset, consisting of 55 unique word problems that target the shortcomings of the next token prediction paradigm of LLMs and require complex non-linear reasoning but only basic arithmetic skills to solve. Our findings demonstrate that the integration of Prolog enables LLMs to achieve high performance on the NLR dataset, which even the most advanced language models (including GPT4) fail to solve using text only.

Navigating the Labyrinth: Evaluating and Enhancing LLMs' Ability to Reason About Search Problems

Recently, Large Language Models (LLMs) attained impressive performance in math and reasoning benchmarks. However, they still often struggle with logic problems and puzzles that are relatively easy for humans. To further investigate this, we introduce a new benchmark, SearchBench, containing 11 unique search problem types, each equipped with automated pipelines to generate an arbitrary number of instances and analyze the feasibility, correctness, and optimality of LLM-generated solutions. We show that even the most advanced LLMs fail to solve these problems end-to-end in text, e.g. GPT4 solves only 1.4%. SearchBench problems require considering multiple pathways to the solution as well as backtracking, posing a significant challenge to auto-regressive models. Instructing LLMs to generate code that solves the problem helps, but only slightly, e.g., GPT4's performance rises to 11.7%. In this work, we show that in-context learning with A* algorithm implementations enhances performance. The full potential of this promoting approach emerges when combined with our proposed Multi-Stage-Multi-Try method, which breaks down the algorithm implementation into two stages and verifies the first stage against unit tests, raising GPT-4's performance above 57%.